Question

Find the height of a cone whose radius of base is 40 cm and curved surface area is 1640 $\pi .$

Answer 1

We have,

Curved surface of cone $=1640\pi$

Now,

$\begin{array}{c}\pi rl=1640\pi \\ \Rightarrow 40\times l=1640\\ \Rightarrow l=\frac{1640}{40}\\ \therefore l=41cm\end{array}$

We know that

$h=\sqrt{l^2-r^2}$

$h=\sqrt{{41}^2-{40}^2}$

$h=\sqrt{1681-1600}$

$h=\sqrt{81}$

$h=9cm$

Hence, this is the answer.